How to draw a flat ellipse surface in Blender with the following known dimensions?
I found a solution! 
Use this code in the blender text editor:

import bpy
import math

#IMPORTANT : set 3d cursor to world origin    
bpy.context.area.spaces[1].cursor_location = (0.0, 0.0, 0.0)

#Add circle curve
bpy.ops.curve.primitive_bezier_circle_add(view_align=False, enter_editmode=False, location=(0, 0, 0), layers=(True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False))

#define variables
a = 10
b = 2
c = 3 # I use the half of c
d = 5

#Calculate width
width = a + b   #or width = a + d + b?

#Calculate horizontal distance from world origin of c
distance = b / 2

#Calculate height c for the circle
#x^2 + y^2 = 1, see Unit Circle
x = (distance / (width / 2)) * math.pi * 0.5  

cCircle = math.sqrt(1 - x**2)

#now we have to scale the height of the circle, so cCircle becomes c. And give its width.
factor = c / cCircle

bpy.ops.transform.resize(value=((width)/2, factor, 1), constraint_axis=(True, True, False), constraint_orientation='GLOBAL', mirror=False, proportional='DISABLED', proportional_edit_falloff='SMOOTH', proportional_size=1)

#Calculate location origin
originX = -((width) / 2 ) + b
originY = 0
originZ = 0

#Set 3d Cursor at Origin location
bpy.context.area.spaces[1].cursor_location = (originX, originY, originZ)

#Set origin to 3d cursor
bpy.ops.object.origin_set(type='ORIGIN_CURSOR')

#Move object to world origin
bpy.ops.transform.translate(value=((width/2) - b, 0, 0), constraint_axis=(True, False, False), constraint_orientation='GLOBAL', mirror=False, proportional='DISABLED', proportional_edit_falloff='SMOOTH', proportional_size=1, release_confirm=True)

#Voila


I hope this helps!